shows that if c' is sounded with a note which makes with it 47 beats in a second, then these beats will fuse into one smooth, continuous sensation, and the notes must be in harmony. What is this note? It is found in this manner: c' is made by 256 vibrations per second, and the note which will make just 47 beats with it in a second must make 256+47 or 303 vibrations in a second. This number of vibrations makes a sound a little lower in pitch than be'. This is the minor third of c'. EXPERIMENT 128.-Now let one sing c' while another sings be', and you will find that these sounds form an interval which is just within the range of harmony. EXPERIMENT 129.-Sing c' and e', then c' and g', and you will have yet more pleasant and smooth sensations. EXPERIMENT 130.—But if one sings c' while another sings d' you have decided discord, an unpleasant rasping sensation in the ears. The reason of this is at once apparent: c' makes 256 while d' makes 288 vibrations in a second, and 288 less 256 gives 32 as the number of beats made in a second; but the table shows that 47 are needed in a second so that they may follow each other quick enough to blend. Making similar calculations throughout five octaves, we have found the nearest consonant intervals for the c of each octave from C to c1V. These are here given. It will be observed that this interval contracts as we ascend the musical scale-a fact which has been well established. The nearest consonant interval of C is its major third. Our experiments in sound have led us into music. We find that fundamental facts and laws of harmony may be explained by physiological laws-by rules according to which our sensations act. Music is the sequence and concourse of sounds made in obedience to these laws. The explanation of many of these may be beyond our power; for the connection existing between æsthetic and moral feelings and sensations which cause them remains behind a veil. But it may be imagined that distant ages may bring forth man so highly organized that he may find his pleasure and pastime in “Untwisting all the chains that tie THE END. List of Apparatus used in the Experiments on Light and Sound, with the prices, as supplied by Samuel Hawkridge, successor to George Wale & Co., Hoboken, New Jersey. Glass cylinder for experiment of the illuminated jet-to be used with plano-convex lens in place of the large flask shown in Fig. 23... Glass prism. Top..... Cake of vermilion paint.. Cake of emerald green paint.. Nuremberg violet, in powder, to be used with gum-water.. 9. Slips of wood and board... 9. Pair of pine rods, for vibrating. 17. Boxes, to be half filled with sand, for supports... 17. Two pine rods, with mirrors.... 76. One C-fork.. 95. Two A-forks, mounted on resonant boxes.. 1 50 50 10 15 15 15 05 $14 85 .$ 05 2 50 25 25 1 00 30 75 2 50 33. Kundt's experiment with whistle and tube containing silica... 15 30 34. Glass tube, 3 feet long, 3 inch in diameter.. 10 57. Long brass spring-cord and resonant box.. 1 50 58. Rotator, with four disks, viz., siren, Crova's, Rood's, and 88. Sonometer..... 81. Resonant glass tube, 1 foot long, 2 inch in diameter. 100. Slinging whistle and 3 feet of large tube..... 88. Violin-bow 112. König's vibrating flame...... 16. Twelve plates of glass, each 6 inches square. 16. Bottle of varnish.. 13. Sand... . . . . 45. Six sheets of linen paper. 05 60 2 50 50 2.50 50 15 10 05 The numbers prefixed to the above list refer to similarly numbered experiments in "Sound" in which these articles are used. SOUND: A Series of Simple, Entertaining, and Inexpensive Experiments in the Phenomena of Sound, for the Use of Students of Every Age. By ALFRED MARSHALL MAYER, Professor of Physics in the Stevens Institute of Technology; Member of the National Academy of Sciences, etc. UNIFORM WITH "LIGHT," FIRST VOLUME OF THE SERIES. Neat 12mo volume, bound in cloth, fully illustrated. Price, $1.00. "It would really be difficult to exaggerate the merit, in the sense of consummate adaptation to its modest end, of the little treatise on 'Sound' which forms the second number of Appletons' 'Experimental Science Series.' The purpose of these hand-books is to teach the youthful student how to make experiments for himself, without the help of a trained operator, and at very little expense. How successful the authors were in attaining that end is attested by the remarkable and constantly-increasing demand for the initial volume. These hand-books of Professor Mayer should be in the hands of every teacher of the young."-New York Sun. "The present work is an admirably clear and interesting collection of experiments, described with just the right amount of abstract information and no more, and placed in progressive order. The recent inventions of the phonograph and microphone lend an extraordinary interest to this whole field of experiment, which makes Professor Mayer's manual especially opportune."-Boston Courier. "Dr. Mayer has written a second beautiful book of experimental science, the subject being 'Sound.' It is a little volume, is surprisingly comprehensive, and, although intended for beginners, contains many pages that will be read with pleasure by those most familiar with the subject."-N. Y. Independent. "Sound is the second volume of the Experimental Science Series.' Like its predecessor, it is deserving of hearty commendation for the number of ingenious and novel experiments by which the scientific principles are illustrated. These little volumes are the best manuals ever written for the use of non-scientific students, and their study will more than repay the labor devoted to them." -Boston Gazette. "An interesting little treatise on 'Sound.' A carefully-prepared price-list of articles needed for tests and experiments adds to the value of the volume."-Boston Evening Transcript. D. APPLETON & CO., PUBLISHERS, 1, 3, & 5 BOND STREET, NEW YORK. |